Find the value of $\frac{(0.5436)^3}{0.017 \times 0.219}$ to 3 significant figures.

Analysis

To solve this problem, we need to perform the arithmetic operations in the correct order: first, calculate the cube of the numerator, then calculate the product in the denominator, and finally perform the division. After obtaining the result, we will round it to 3 significant figures.

Concept

1. Exponents: $(0.5436)^3 = 0.5436 \times 0.5436 \times 0.5436$
2. Multiplication: Calculate the product of the two numbers in the denominator.
3. Division: Divide the result of the cube by the result of the product.
4. Significant Figures: When rounding to 3 significant figures, we count three digits starting from the first non-zero digit.

Step-by-Step Solution

Step 1: Calculate the numerator $(0.5436)^3 = 0.5436 \times 0.5436 \times 0.5436$ $0.5436 \times 0.5436 \approx 0.29550096$ $0.29550096 \times 0.5436 \approx 0.1606343$

Step 2: Calculate the denominator $0.017 \times 0.219 = 0.003723$

Step 3: Perform the division $\frac{0.1606343}{0.003723} \approx 43.146467...$

Step 4: Round to 3 significant figures The first three digits are 4, 3, and 1. The next digit is 4, which is less than 5, so we keep the 1 as it is. Result $\approx 43.1$

Conclusion

Comparing our result with the options provided, we see that 43.1 corresponds to option B.

Exam Tip

When dealing with decimals in JAMB, if you are not allowed a calculator, try converting the decimals to standard form (e.g., $5.436 \times 10^{-1}$) before multiplying. This helps prevent errors with decimal point placement. Also, always perform a quick "sanity check" by rounding the numbers to one significant figure first to estimate the magnitude of your answer (e.g., $0.5^3 / (0.02 \times 0.2) = 0.125 / 0.004 \approx 31$), which helps you spot if your calculated answer is way off.